The compositions of stars are a critical diagnostic tool for many topics in astronomy such as the evolution of our Galaxy, the formation of planets, and the uniqueness of the Sun. Previous spectroscopic measurements indicate a large intrinsic variation in the elemental abundance patterns of stars with similar overall metal content. However, systematic errors arising from inaccuracies in stellar models are known to be a limiting factor in such studies, and thus it is uncertain to what extent the observed diversity of stellar abundance patterns is real. Here we report the abundances of 30 elements with precisions of 2% for 79 Sun-like stars within 100 parsecs. Systematic errors are minimized in this study by focusing on solar twin stars and performing a line-by-line differential analysis using high-resolution, high-signal-to-noise spectra. We resolve [X/Fe] abundance trends in galactic chemical evolution at precisions of 10^-3 dex Gyr^-1 and reveal that stars with similar ages and metallicities have nearly identical abundance patterns. Contrary to previous results, we find that the ratios of carbon-to-oxygen and magnesium-to-silicon are homogeneous to within 10% throughout the solar neighborhood, implying that exoplanets may exhibit much less compositional diversity than previously thought. Finally, we demonstrate that the Sun has a subtle deficiency in refractory material relative to ~95% of solar twins, suggesting a possible signpost for planetary systems like our own.